One of the most commonly used analytical tools for studying both standard and non-standard Hele–Shaw flow is linear stability analysis. For the standard configuration, [1]} showed that modes of perturbation to the circular solution becomes successively unstable as the bubble expands, predicting the most unstable wave number for a given bubble radius. Further, linear stability analysis has also been used to derive injection rates to control [2]} or minimise [3]} the development of viscous fingering. For non-standard Hele–Shaw flow, linear stability analysis gives insight into how manipulating the geometry of the cell influences the development of viscous fingers, including when the plates are tapered [4]}, [5]}, rotating [6]}, or are being separated [7]}. While linear stability analysis is a flexible tool that leads to analytic predictions, it only provides an accurate description of solutions for small time. As such, this restriction increases the need for flexible and accurate numerical methods that can be used to understand the full nonlinear behaviour of these problems.
